Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods
In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equil...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/5051248 |
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| _version_ | 1850161926404833280 |
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| author | Sara Bidah Omar Zakary Mostafa Rachik |
| author_facet | Sara Bidah Omar Zakary Mostafa Rachik |
| author_sort | Sara Bidah |
| collection | DOAJ |
| description | In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling. |
| format | Article |
| id | doaj-art-fd6e3b8d97cd48a1b1b7f26745e13a6b |
| institution | OA Journals |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-fd6e3b8d97cd48a1b1b7f26745e13a6b2025-08-20T02:22:40ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/50512485051248Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling MethodsSara Bidah0Omar Zakary1Mostafa Rachik2Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Informatics, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Informatics, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modelling and Simulation, Department of Mathematics and Informatics, Faculty of Sciences Ben M’Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, MoroccoIn this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling.http://dx.doi.org/10.1155/2020/5051248 |
| spellingShingle | Sara Bidah Omar Zakary Mostafa Rachik Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods International Journal of Differential Equations |
| title | Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods |
| title_full | Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods |
| title_fullStr | Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods |
| title_full_unstemmed | Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods |
| title_short | Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods |
| title_sort | stability and global sensitivity analysis for an agree disagree model partial rank correlation coefficient and latin hypercube sampling methods |
| url | http://dx.doi.org/10.1155/2020/5051248 |
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